Find Least Common Multiple of 86, 96 and 54 using prime factorisation method.
Answer
LCM( 86, 96, 54 ) = 37152
Explanation
Step 1: Write down factorisation of each number:
86 = 2 · 43
96 = 2 · 2 · 2 · 2 · 2 · 3
54 = 2 · 3 · 3 · 3
Step 2 : Match primes vertically:
| 86 | = | 2 | · | 43 | ||||||||||||||
| 96 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | ||||||
| 54 | = | 2 | · | 3 | · | 3 | · | 3 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 86 | = | 2 | · | 43 | ||||||||||||||||
| 96 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | ||||||||
| 54 | = | 2 | · | 3 | · | 3 | · | 3 | ||||||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 3 | · | 43 | = | 37152 |
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.
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